Twist periodic solutions of second order singular differential equations (Q1022986)

By definition, a periodic solution of a second order ODE is a twist solution if one of the nonlinear coefficients of the Birkhoff normal form of the Poincaré map is different from zero. A twist solution is in particular stable in the sense of Lyapunov. Generally speaking, the twist character of a periodic solution is determined by the third-order expansion of the Poincaré map, the so-called third-order approximation method. This paper continues the study initiated in previous works by the reviewer and provides new stability criteria for equations with repulsive singularities. The proofs involve careful estimates of the rotation number and the radial coordinate of the linerized equation.